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arXiv · 2507.12626

Geometric Theory of Ising Machines

Andrew G. Moore·Zachary Richey·Isaac K. Martin
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Abstract

We contribute to the mathematical theory of the design of low temperature Ising machines, a type of experimental probabilistic computing device implementing the Ising model. Encoding the output of a function in the ground state of a physical system allows efficient and distributed computation, but the design of the energy function is a difficult puzzle. We introduce a diagrammatic device that allows us to visualize the decision boundaries for Ising circuits. It is then used to prove two results: (1) Ising circuits are a generalization of 1-NN classifiers with a certain special structure, and (2) Elimination of local minima in the energy landscape can be formulated as a linear programming problem.

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Andrew G. Moore, Zachary Richey, Isaac K. Martin. 2025-07-16. Geometric Theory of Ising Machines. https://arxiv.org/abs/2507.12626

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